beta = 1E-6; % smoothness factor

% read data, data is already given on equidistant grid
[ X, F ] = textread ( 'filter1d.csv', '%f,%f' );
[ N, M ] = size ( X );

% compute gridwidth
h = ( X ( N ) - X ( 1 ) ) / ( N - 1 );
h2 = h * h;

% reset
L = zeros ( N, N );
r = zeros ( 1, N );

% fill matrix and right hand side
for i = 1 : N
  if i == 1 | i == N
    % point on boundary
    L ( i, i ) = 1;
    r ( i ) = F ( i );
  else
    % point in interior
    L ( i, i ) = 2 * beta / h2 + 1;
    L ( i, i - 1 ) = - beta / h2;
    L ( i, i + 1 ) = - beta / h2;     
    r ( i ) = F ( i );
  end
end

% solve linear equation system
U = L \ r';

% plot original and smoothed profile
plot ( X, F, X, U );